Demographics for all included participants.
| Demographics | ||||
| Summary | ||||
| N | Age (years) | Education (years) | Sex (M/F/O) | EHI |
|---|---|---|---|---|
| 844 | 29.08 (6.03) | 14.38 (2.48) | 441/391/12 | 5.09 (79.37) |
| Race | n |
|---|---|
| White | 606 |
| Black or African American | 82 |
| Multiple | 76 |
| Asian | 69 |
| American Indian or Alaska Native | 5 |
| Native Hawaiian or Other Pacific Islander | 3 |
| Other | 3 |
| Hispanic ethnicity | n |
|---|---|
| No | 744 |
| Yes | 100 |
Demographics for included participants, by handedness group (EHI bins).
| Handedness | N | Age (years) | Education (years) | Sex (M/F/O) | EHI |
|---|---|---|---|---|---|
| Left | 331 | 28.84 (6.1) | 14.45 (2.39) | 170/157/4 | -81.61 (19.27) |
| Mixed | 135 | 28.83 (6.17) | 14.58 (2.6) | 77/56/2 | -8.89 (26.49) |
| Right | 378 | 29.38 (5.93) | 14.24 (2.5) | 194/178/6 | 86.01 (16.61) |
| Left: (EHI <= -40) | Mixed: (-40 < EHI < 40) | Right: (EHI >= 40) | |||||
Do we find an interaction of field x level x handedness, when
handedness is binned as left (EHI <= -40) or right (EHI > +40)?
Summary. For reaction time, we find the critical interaction in the predicted direction (11.67ms, 95% CI [0.65, 22.69], p = .019, one-sided). Left handers show 15.64ms LVF global bias (95% CI [7.61, 23.67]), and right handers 27.31ms (95% CI [19.80, 34.81]). Mixed handers (not included in the categorical interaction analysis) show a LVF global bias of 21.66ms (95% CI [9.09, 34.23]).
For accuracy, we find no significant interaction of field by level by handedness (OR = 0.90, 95% CI [0.70, 1.16], p = .42; where OR < 1 means greater LVF global bias for left handers). Point estimates of LVF global bias hardly differ between left handers (OR = 1.95, 95% CI [1.62, 2.35]) and right handers (OR = 1.77, 95% CI [1.49, 2.10]). For mixed handers (not included in the categorical interaction analysis), the point estimate is 1.10 (95% CI [0.82, 1.47])
Error bars show 95% CI.
Reaction time is modeled as a linear effect of field, level, and
handedness, using data from every target-present trial with a “go”
response:
lmer( rt ~ field*level*handedness + (1 | subject) )
| Field by level by handedness interaction (RT) | |||||||
| ANOVA: compare models with vs. without interaction term | |||||||
| npar | AIC | BIC | logLik | deviance | Chisq | Df | p.value1 |
|---|---|---|---|---|---|---|---|
| 9 | 1,166,282.858 | 1,166,367.139 | −583,132.429 | 1,166,264.858 | - | - | - |
| 10 | 1,166,280.551 | 1,166,374.197 | −583,130.276 | 1,166,260.551 | 4.307 | 1 | .038 |
| 1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html) | |||||||
| Field by level by handedness interaction (RT) | |||||||||
| Compare effect estimate to zero with emmeans() | |||||||||
| field_consec | level_consec | handedness_consec | estimate1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|---|
| LVF - RVF | Local - Global | Right - Left | 11.666 | 5.622 | Inf | 0.648 | 22.685 | 2.075 | .038 |
| 1 A positive number means LVF global bias is stronger in right handers (as predicted by AAH) | |||||||||
| 2 Z-approximation | |||||||||
| 3 Confidence level: 95% | |||||||||
| 4 Two-sided | |||||||||
| LVF Global bias by handedness bin (RT) | |||||||||
| field_consec | level_consec | handedness | estimate1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|---|
| LVF - RVF | Local - Global | Left | 15.641 | 4.096 | Inf | 7.613 | 23.669 | 3.819 | .0001 |
| LVF - RVF | Local - Global | Mixed | 21.658 | 6.414 | Inf | 9.087 | 34.228 | 3.377 | .0007 |
| LVF - RVF | Local - Global | Right | 27.307 | 3.829 | Inf | 19.802 | 34.812 | 7.131 | <.0001 |
| 1 A positive number means global bias (faster RT for global) | |||||||||
| 2 Z-approximation | |||||||||
| 3 Confidence level: 95% | |||||||||
| 4 Two-sided, uncorrected | |||||||||
| Field by level interaction (RT) | |||||
| Old-school Omnibus F-test | |||||
| term | df | sumsq | meansq | statistic | p.value |
|---|---|---|---|---|---|
| field | 1 | 1,664,691.722 | 1,664,691.722 | 23.612 | <.0001 |
| level | 1 | 9,626,122.373 | 9,626,122.373 | 136.54 | <.0001 |
| handedness | 1 | 10,185,712.46 | 10,185,712.46 | 144.477 | <.0001 |
| field:level | 1 | 2,730,949.837 | 2,730,949.837 | 38.737 | <.0001 |
| field:handedness | 1 | 1,505,316.949 | 1,505,316.949 | 21.352 | <.0001 |
| level:handedness | 1 | 12,247.994 | 12,247.994 | 0.174 | .677 |
| field:level:handedness | 1 | 127,954.685 | 127,954.685 | 1.815 | .178 |
| Residuals | 86,205 | 6,077,502,195.866 | 70,500.576 | - | - |
summary(rt_model_2bins)
## Linear mixed model fit by REML ['lmerMod']
## Formula: rt ~ field * level * handedness + (1 | subject)
## Data: aah_for_rt_model_2bins
##
## REML criterion at convergence: 1166226.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.871042 -0.589962 -0.165354 0.361143 7.634801
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 28355.6 168.391
## Residual 42345.3 205.780
## Number of obs: 86213, groups: subject, 709
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 663.50167 9.47901 69.99697
## fieldLVF -25.29475 2.87911 -8.78560
## levelLocal 13.71496 2.91027 4.71261
## handednessRight 18.61377 12.98209 1.43380
## fieldLVF:levelLocal 15.64117 4.10675 3.80865
## fieldLVF:handednessRight 10.27036 3.94550 2.60306
## levelLocal:handednessRight -6.47365 3.98194 -1.62575
## fieldLVF:levelLocal:handednessRight 11.66629 5.62176 2.07520
##
## Correlation of Fixed Effects:
## (Intr) fldLVF lvlLcl hnddnR flLVF:L fLVF:R lvlL:R
## fieldLVF -0.153
## levelLocal -0.152 0.499
## hnddnssRght -0.730 0.112 0.111
## fldLVF:lvlL 0.107 -0.701 -0.707 -0.078
## fldLVF:hndR 0.112 -0.730 -0.364 -0.153 0.512
## lvlLcl:hndR 0.111 -0.365 -0.731 -0.152 0.517 0.500
## fldLVF:lL:R -0.079 0.512 0.517 0.108 -0.731 -0.702 -0.707
Error bars show 95% CI.
Accuracy is modeled as a binomial effect of field, level, and
handedness, using binary correct/incorrect data from every
target-present trial:
glmer( correct ~ field*level*handedness + (1 | subject), family = "binomial" )
| Field by level by handedness interaction (Accuracy) | |||||||
| ANOVA: compare models with vs. without interaction term | |||||||
| npar | AIC | BIC | logLik | deviance | Chisq | Df | p.value1 |
|---|---|---|---|---|---|---|---|
| 8 | 32,836.316 | 32,911.643 | −16,410.158 | 32,820.316 | - | - | - |
| 9 | 32,837.667 | 32,922.41 | −16,409.833 | 32,819.667 | 0.649 | 1 | .42 |
| 1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html) | |||||||
| Field by level by handedness interaction (Accuracy) | ||||||||||
| Compare effect estimate to zero with emmeans() | ||||||||||
| field_consec | level_consec | handedness_consec | odds.ratio1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | null | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|---|---|
| LVF / RVF | Global / Local | Right / Left | 0.899 | 0.118 | Inf | 0.696 | 1.162 | 1 | −0.814 | .416 |
| 1 Backtransformed to odds ratio from log odds ratio (tests are performed on log odds ratio scale). A ratio > 1 means global bias is stronger in the LVF for right handers (predicted by AAH) | ||||||||||
| 2 'Inf' df is expected when emmeans does logistic regression. See emmeans FAQ: https://cran.r-project.org/web/packages/emmeans/vignettes/FAQs.html#asymp. | ||||||||||
| 3 Confidence level: 95% | ||||||||||
| 4 Two-sided | ||||||||||
| LVF Global bias by handedness bin (Accuracy) | ||||||||||
| Compare effect estimate to zero with emmeans() | ||||||||||
| field_consec | level_consec | handedness | odds.ratio1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | null | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|---|---|
| LVF / RVF | Global / Local | Left | 1.954 | 0.185 | Inf | 1.623 | 2.353 | 1 | 7.063 | <.0001 |
| LVF / RVF | Global / Local | Mixed | 1.097 | 0.162 | Inf | 0.821 | 1.465 | 1 | 0.626 | .532 |
| LVF / RVF | Global / Local | Right | 1.766 | 0.154 | Inf | 1.488 | 2.095 | 1 | 6.514 | <.0001 |
| 1 Backtransformed to odds ratio from log odds ratio (tests are performed on log odds ratio scale). A ratio > 1 means global bias is stronger in the LVF, as predicted for right handers. Mixed handers' global bias is shown here, but their data was not included in the binomial model. | ||||||||||
| 2 'Inf' df is expected when emmeans does logistic regression. See emmeans FAQ: https://cran.r-project.org/web/packages/emmeans/vignettes/FAQs.html#asymp. | ||||||||||
| 3 Confidence level: 95% | ||||||||||
| 4 Two-sided | ||||||||||
summary(acc_model_2bins)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ field * level * handedness + (1 | subject)
## Data: aah_for_acc_model_2bins
##
## AIC BIC logLik deviance df.resid
## 32837.7 32922.4 -16409.8 32819.7 90743
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -12.046183 0.123597 0.170659 0.240743 1.070559
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 1.03569 1.01769
## Number of obs: 90752, groups: subject, 709
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 3.1227080 0.0719596 43.39530
## fieldLVF -0.1101649 0.0563127 -1.95631
## levelGlobal 0.4277909 0.0630223 6.78793
## handednessRight 0.1047397 0.0983966 1.06446
## fieldLVF:levelGlobal 0.6731050 0.0962270 6.99497
## fieldLVF:handednessRight -0.0341608 0.0784866 -0.43524
## levelGlobal:handednessRight -0.1561983 0.0867458 -1.80064
## fieldLVF:levelGlobal:handednessRight -0.1065265 0.1308698 -0.81399
## Pr(>|z|)
## (Intercept) < 2.22e-16 ***
## fieldLVF 0.050429 .
## levelGlobal 0.0000000000113752 ***
## handednessRight 0.287118
## fieldLVF:levelGlobal 0.0000000000026532 ***
## fieldLVF:handednessRight 0.663386
## levelGlobal:handednessRight 0.071759 .
## fieldLVF:levelGlobal:handednessRight 0.415651
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fldLVF lvlGlb hnddnR flLVF:G fLVF:R lvlG:R
## fieldLVF -0.410
## levelGlobal -0.361 0.467
## hnddnssRght -0.718 0.301 0.266
## fldLVF:lvlG 0.244 -0.589 -0.656 -0.180
## fldLVF:hndR 0.295 -0.720 -0.338 -0.421 0.426
## lvlGlbl:hnR 0.264 -0.342 -0.730 -0.377 0.481 0.478
## fldLVF:lG:R -0.181 0.436 0.487 0.257 -0.740 -0.605 -0.667
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00965947 (tol = 0.002, component 1)
Using the bobyqa optimizer alone gives virtually the same
results.
summary(acc_model_2bins_bobyqa)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ field * level * handedness + (1 | subject)
## Data: aah_for_acc_model_2bins
## Control: glmerControl(optimizer = c("bobyqa"))
##
## AIC BIC logLik deviance df.resid
## 32837.7 32922.4 -16409.8 32819.7 90743
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -12.045085 0.123596 0.170659 0.240752 1.070436
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 1.03554 1.01762
## Number of obs: 90752, groups: subject, 709
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 3.1227181 0.0717392 43.52878
## fieldLVF -0.1101583 0.0561263 -1.96269
## levelGlobal 0.4271459 0.0626393 6.81913
## handednessRight 0.1047658 0.0980956 1.06800
## fieldLVF:levelGlobal 0.6734926 0.0955733 7.04687
## fieldLVF:handednessRight -0.0341812 0.0782540 -0.43680
## levelGlobal:handednessRight -0.1555689 0.0862525 -1.80364
## fieldLVF:levelGlobal:handednessRight -0.1068799 0.1300024 -0.82214
## Pr(>|z|)
## (Intercept) < 2.22e-16 ***
## fieldLVF 0.049683 *
## levelGlobal 0.0000000000091593 ***
## handednessRight 0.285522
## fieldLVF:levelGlobal 0.0000000000018299 ***
## fieldLVF:handednessRight 0.662258
## levelGlobal:handednessRight 0.071287 .
## fieldLVF:levelGlobal:handednessRight 0.410999
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fldLVF lvlGlb hnddnR flLVF:G fLVF:R lvlG:R
## fieldLVF -0.407
## levelGlobal -0.357 0.463
## hnddnssRght -0.716 0.298 0.263
## fldLVF:lvlG 0.241 -0.585 -0.653 -0.176
## fldLVF:hndR 0.292 -0.719 -0.334 -0.419 0.422
## lvlGlbl:hnR 0.260 -0.338 -0.727 -0.375 0.476 0.475
## fldLVF:lG:R -0.177 0.432 0.482 0.254 -0.737 -0.602 -0.664
Do we find an interaction of field x level x handedness (continuous
EHI score)?
Summary. For reaction time, we find the critical interaction in the predicted direction (.067ms per EHI unit, 95% CI [0.003, 0.13], p = .020, one-sided). Estimated global bias is 13.32ms lower for strong left handers (EHI -100: 14.82ms, 95% CI [6.48, 23.17]) than for strong right handers (EHI +100: 28.14ms, 95% CI [20.31, 35.98]).
For accuracy, we find no significant interaction of field by level by EHI (Beta = 0.0002 logodds per EHI unit, 95% CI [-0.001, 0.002], p = .81). Estimated LVF global bias hardly differs for strong left handers (EHI -100: OR = 1.67, 95% CI [1.37, 2.03]) and strong right handers (EHI +100: OR = 1.73, 95% CI [1.45, 2.07]).
Model RT as a linear effect of field, level, and EHI (continuous):
rt_model_ehi <- lmer( rt ~ field*level*ehi + (1 | subject) )
| Field by level by ehi interaction (RT) | |||||||
| ANOVA: compare models with vs. without interaction term | |||||||
| npar | AIC | BIC | logLik | deviance | Chisq | Df | p.value1 |
|---|---|---|---|---|---|---|---|
| 9 | 1,387,640.958 | 1,387,726.807 | −693,811.479 | 1,387,622.958 | - | - | - |
| 10 | 1,387,638.71 | 1,387,734.097 | −693,809.355 | 1,387,618.71 | 4.248 | 1 | .039 |
| 1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html) | |||||||
| Field by level interaction (RT) | ||||||||
| Compare effect estimate to zero with emmeans() | ||||||||
| field_consec | level_consec | estimate1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|
| RVF - LVF | Global - Local | 0.067 | 0.032 | Inf | 0.003 | 0.13 | 2.061 | .039 |
| 1 A positive number means global bias is stronger in LVF for right handers (as predicted by AAH), in ms per EHI unit (-100 to 100). Multiply this value by 200 to get the estimated difference in LVF global bias for strong left vs. right handers. | ||||||||
| 2 Z-approximation | ||||||||
| 3 Confidence level: 95 | ||||||||
| 4 Two-sided | ||||||||
| Field by level interaction (RT) | |||||||
| Compare effect estimate to zero with emmeans() | |||||||
| contrast | estimate1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|
| LVF Local - LVF Global | 0.033 | 0.023 | Inf | −0.025 | 0.092 | 1.459 | .463 |
| RVF Local - RVF Global | −0.033 | 0.023 | Inf | −0.092 | 0.026 | −1.454 | .465 |
| 1 A positive number means more global bias for right handers, in ms per EHI unit (-100 to 100) | |||||||
| 2 Z-approximation | |||||||
| 3 Confidence level: 95% | |||||||
| 4 Two-sided | |||||||
| Slope of EHI and RT by field and level | ||||||||
| Compare effect estimate to zero with emmeans() | ||||||||
| field | level | ehi.trend1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|
| LVF | Local | 0.219 | 0.075 | Inf | 0.073 | 0.366 | 2.93 | .003 |
| RVF | Local | 0.096 | 0.075 | Inf | −0.05 | 0.243 | 1.288 | .198 |
| LVF | Global | 0.186 | 0.075 | Inf | 0.039 | 0.332 | 2.487 | .013 |
| RVF | Global | 0.13 | 0.075 | Inf | −0.017 | 0.276 | 1.734 | .083 |
| 1 A positive number means slower RTs for right handers, in ms per EHI unit (-100 to 100). | ||||||||
| 2 Z-approximation | ||||||||
| 3 Confidence level: 95% | ||||||||
| 4 Two-sided | ||||||||
| Estimated LVF global bias, by EHI score | |||||||||
| field_consec | level_consec | ehi1 | estimate2 | SE | df | asymp.LCL | asymp.UCL | z.ratio | p.value |
|---|---|---|---|---|---|---|---|---|---|
| RVF - LVF | Global - Local | −100 | 14.822 | 4.257 | Inf | 6.479 | 23.166 | 3.482 | .0005 |
| RVF - LVF | Global - Local | 0 | 21.483 | 2.569 | Inf | 16.447 | 26.519 | 8.361 | <.0001 |
| RVF - LVF | Global - Local | 100 | 28.144 | 3.996 | Inf | 20.311 | 35.976 | 7.042 | <.0001 |
| 1 Strong left hander: -100; Mixed hander: 0; Strong right hander: +100 | |||||||||
| 2 Estimated LVF global bias (ms); a positive number means LVF global bias | |||||||||
| Estimated global bias by field, by EHI score | ||||||||
| contrast | ehi | estimate1 | SE | df | asymp.LCL | asymp.UCL | z.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| LVF Local - LVF Global | −100 | 29.412 | 3.009 | Inf | 21.683 | 37.141 | 9.776 | <.0001 |
| RVF Local - RVF Global | −100 | 14.59 | 3.016 | Inf | 6.841 | 22.339 | 4.837 | <.0001 |
| LVF Local - LVF Global | 0 | 32.743 | 1.816 | Inf | 28.077 | 37.409 | 18.028 | <.0001 |
| RVF Local - RVF Global | 0 | 11.26 | 1.82 | Inf | 6.586 | 15.935 | 6.188 | <.0001 |
| LVF Local - LVF Global | 100 | 36.074 | 2.824 | Inf | 28.82 | 43.328 | 12.775 | <.0001 |
| RVF Local - RVF Global | 100 | 7.93 | 2.83 | Inf | 0.66 | 15.201 | 2.802 | .026 |
| 1 Estimated global bias (ms); a positive number means global bias | ||||||||
| Reaction time by field and level, by EHI score | |||||
| field | level | ehi | prediction1 | asymp.LCL | asymp.UCL |
|---|---|---|---|---|---|
| LVF | Local | −100 | 658.263 | 638.967 | 677.559 |
| RVF | Local | −100 | 667.869 | 648.575 | 687.163 |
| LVF | Global | −100 | 628.851 | 609.576 | 648.126 |
| RVF | Global | −100 | 653.279 | 633.997 | 672.561 |
| LVF | Local | 0 | 680.17 | 668.522 | 691.818 |
| RVF | Local | 0 | 677.494 | 665.848 | 689.14 |
| LVF | Global | 0 | 647.427 | 635.791 | 659.063 |
| RVF | Global | 0 | 666.234 | 654.594 | 677.874 |
| LVF | Local | 100 | 702.077 | 683.953 | 720.201 |
| RVF | Local | 100 | 687.119 | 668.998 | 705.24 |
| LVF | Global | 100 | 666.002 | 647.895 | 684.11 |
| RVF | Global | 100 | 679.189 | 661.074 | 697.303 |
| 1 Reaction time (ms) | |||||
\[
28.144 - 14.822 = 13.322ms \\
13.322/200 = 0.067ms / EHI unit
\] The model estimates that an average strong right hander (EHI
+100) will have 13.32ms more LVF global bias than a
strong left hander (EHI -100). Each unit change in EHI (-100:100)
corresponds to a 0.067ms difference in LVF global bias.
This is also the slope estimate given by the summary function:
summary(rt_model_ehi)
## Linear mixed model fit by REML ['lmerMod']
## Formula: rt ~ field:level:ehi + field:level + field:ehi + level:ehi +
## field + level + ehi + (1 | subject)
## Data: aah_for_rt_ehi_model
##
## REML criterion at convergence: 1387626.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.879612 -0.590631 -0.167132 0.363313 7.653749
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 28269.4 168.135
## Residual 42128.7 205.253
## Number of obs: 102615, groups: subject, 844
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 680.1697334 5.9429525 114.44980
## fieldRVF -2.6755865 1.8307862 -1.46144
## levelGlobal -32.7431087 1.8162558 -18.02781
## ehi 0.2190687 0.0747656 2.93007
## fieldRVF:levelGlobal 21.4828945 2.5694569 8.36087
## fieldRVF:ehi -0.1228165 0.0230212 -5.33493
## levelGlobal:ehi -0.0333102 0.0228331 -1.45886
## fieldRVF:levelGlobal:ehi 0.0666075 0.0323174 2.06104
##
## Correlation of Fixed Effects:
## (Intr) fldRVF lvlGlb ehi flRVF:G flRVF: lvlGl:
## fieldRVF -0.155
## levelGlobal -0.156 0.506
## ehi -0.064 0.010 0.010
## fldRVF:lvlG 0.110 -0.713 -0.706 -0.007
## fieldRVF:eh 0.010 -0.067 -0.033 -0.154 0.047
## levelGlbl:h 0.010 -0.033 -0.065 -0.156 0.046 0.506
## fldRVF:lvG: -0.007 0.047 0.046 0.110 -0.065 -0.712 -0.706
Model accuracy as a binomial effect of field, level, and EHI
(continuous):
acc_ehi_model <- glmer( rt ~ field*level*ehi + (1 | subject), family = "binomial" )
| Field by level by EHI interaction (Accuracy) | |||||||
| ANOVA: compare models with vs. without interaction term | |||||||
| npar | AIC | BIC | logLik | deviance | Chisq | Df | p.value1 |
|---|---|---|---|---|---|---|---|
| 8 | 39,111.468 | 39,188.189 | −19,547.734 | 39,095.468 | - | - | - |
| 9 | 39,113.409 | 39,199.72 | −19,547.704 | 39,095.409 | 0.059 | 1 | .808 |
| 1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html) | |||||||
| Field by level by EHI interaction (Accuracy) | ||||||||
| Compare effect estimate to zero with emmeans() | ||||||||
| field_consec | level_consec | estimate1 | SE | df | asymp.LCL2 | asymp.UCL2 | z.ratio | p.value3 |
|---|---|---|---|---|---|---|---|---|
| RVF - LVF | Local - Global | 0.0002 | 0.0007 | Inf | −0.0013 | 0.0017 | 0.2491 | .803 |
| 1 A positive number means global bias is stronger in LVF for right handers (as predicted), in logodds per EHI unit (-100 to 100). Multiply this value by 200 to get the estimated difference in LVF global bias for strong left vs. right handers. | ||||||||
| 2 Confidence level: 95% (two-sided) | ||||||||
| 3 Two-sided | ||||||||
| Field by level interaction (Accuracy) | |||||||
| contrast | estimate1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|
| LVF Global - LVF Local | −0.001 | 0.0006 | Inf | −0.0021 | 0.0001 | −1.8003 | .072 |
| RVF Global - RVF Local | −0.0012 | 0.0005 | Inf | −0.0022 | −0.0002 | −2.3594 | .018 |
| 1 A positive number means more global bias, in logodds per EHI unit (-100 to 100) | |||||||
| 2 Z-approximation | |||||||
| 3 Confidence level: 95% | |||||||
| 4 Two-sided, uncorrected | |||||||
| Slope of EHI and Accuracy by field and level | ||||||||
| Compare effect estimate to zero with emmeans() | ||||||||
| field | level | ehi.trend1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|
| LVF | Global | −0.0007 | 0.0007 | Inf | −0.002 | 0.0006 | −1.0258 | .305 |
| RVF | Global | −0.0006 | 0.0006 | Inf | −0.0018 | 0.0006 | −0.9557 | .339 |
| LVF | Local | 0.0003 | 0.0006 | Inf | −0.0008 | 0.0014 | 0.5793 | .562 |
| RVF | Local | 0.0006 | 0.0006 | Inf | −0.0005 | 0.0017 | 1.0666 | .286 |
| 1 A positive number means higher accuracy for right handers, in logodds per EHI unit (-100 to 100). | ||||||||
| 2 Z-approximation | ||||||||
| 3 Confidence level: 95% | ||||||||
| 4 Two-sided | ||||||||
| Estimated LVF global bias, by EHI score | ||||||||||
| field_consec | level_consec | ehi1 | odds.ratio2 | SE | df | asymp.LCL | asymp.UCL | null | z.ratio | p.value |
|---|---|---|---|---|---|---|---|---|---|---|
| RVF / LVF | Local / Global | -100 | 1.67 | 0.166 | Inf | 1.374 | 2.028 | 1 | 5.164 | <.0001 |
| RVF / LVF | Local / Global | 0 | 1.701 | 0.101 | Inf | 1.514 | 1.911 | 1 | 8.942 | <.0001 |
| RVF / LVF | Local / Global | 100 | 1.733 | 0.159 | Inf | 1.448 | 2.074 | 1 | 5.996 | <.0001 |
| 1 Strong left hander: -100; Mixed hander: 0; Strong right hander: +100 | ||||||||||
| 2 Estimated LVF global bias. An odds ratio > 1 means LVF global bias. | ||||||||||
| Estimated global bias by field, by EHI score | |||||||||
| contrast | ehi | odds.ratio1 | SE | df | asymp.LCL | asymp.UCL | null | z.ratio | p.value |
|---|---|---|---|---|---|---|---|---|---|
| LVF Global / LVF Local | -100 | 2.83 | 0.209 | Inf | 2.341 | 3.422 | 1 | 14.075 | <.0001 |
| RVF Global / RVF Local | -100 | 1.695 | 0.112 | Inf | 1.429 | 2.01 | 1 | 7.953 | <.0001 |
| LVF Global / LVF Local | 0 | 2.561 | 0.113 | Inf | 2.287 | 2.868 | 1 | 21.336 | <.0001 |
| RVF Global / RVF Local | 0 | 1.506 | 0.06 | Inf | 1.359 | 1.668 | 1 | 10.266 | <.0001 |
| LVF Global / LVF Local | 100 | 2.317 | 0.157 | Inf | 1.947 | 2.758 | 1 | 12.409 | <.0001 |
| RVF Global / RVF Local | 100 | 1.337 | 0.083 | Inf | 1.141 | 1.567 | 1 | 4.697 | <.0001 |
| 1 Estimated global bias. An odds ratio > 1 means global bias. | |||||||||
| Accurracy by field and level, by EHI score | |||||
| field | level | ehi | prob1 | asymp.LCL | asymp.UCL |
|---|---|---|---|---|---|
| LVF | Global | −100 | 0.983 | 0.98 | 0.986 |
| RVF | Global | −100 | 0.974 | 0.97 | 0.978 |
| LVF | Local | −100 | 0.953 | 0.947 | 0.96 |
| RVF | Local | −100 | 0.957 | 0.951 | 0.963 |
| LVF | Global | 0 | 0.982 | 0.98 | 0.984 |
| RVF | Global | 0 | 0.973 | 0.97 | 0.975 |
| LVF | Local | 0 | 0.955 | 0.951 | 0.959 |
| RVF | Local | 0 | 0.959 | 0.956 | 0.963 |
| LVF | Global | 100 | 0.981 | 0.977 | 0.983 |
| RVF | Global | 100 | 0.971 | 0.967 | 0.975 |
| LVF | Local | 100 | 0.956 | 0.95 | 0.962 |
| RVF | Local | 100 | 0.962 | 0.956 | 0.967 |
| 1 Accuracy (% correct) | |||||
\[
log(1.73) = .548
\] \[
log(1.67) = .513
\] \[
log(1.73) - log(1.67) = .0353
\] \[
.0353 / 200 = -0.000185 logodds / EHI unit
\] The model estimates that a strong right hander (EHI +100) will
have 1.73/1.67 = 1.04 greater odds of correctness for LVF global stimuli
versus a strong left hander (EHI -100). Each unit change in EHI
(-100:100) corresponds to a 0.0002 (logodds) difference
in LVF global bias. This matches the slope estimate given by the summary
function:
summary(acc_model_ehi)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ field * level * ehi + (1 | subject)
## Data: aah_for_acc_ehi_model
##
## AIC BIC logLik deviance df.resid
## 39113.4 39199.7 -19547.7 39095.4 108023
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -11.748088 0.117364 0.168282 0.238851 1.067892
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 1.05841 1.02879
## Number of obs: 108032, groups: subject, 844
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.9930184017 0.0532670291 74.96229 < 2e-16 ***
## fieldRVF -0.4209327473 0.0474500751 -8.87107 < 2e-16 ***
## levelLocal -0.9403339363 0.0440725615 -21.33604 < 2e-16 ***
## ehi -0.0006744722 0.0006575342 -1.02576 0.305005
## fieldRVF:levelLocal 0.5311871060 0.0594032015 8.94206 < 2e-16 ***
## fieldRVF:ehi 0.0000955515 0.0005978575 0.15982 0.873020
## levelLocal:ehi 0.0009994867 0.0005551631 1.80035 0.071806 .
## fieldRVF:levelLocal:ehi 0.0001864551 0.0007484763 0.24911 0.803273
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fldRVF lvlLcl ehi flRVF:L flRVF: lvlLc:
## fieldRVF -0.528
## levelLocal -0.575 0.636
## ehi -0.084 0.058 0.064
## fldRVF:lvlL 0.423 -0.799 -0.742 -0.046
## fieldRVF:eh 0.057 -0.105 -0.069 -0.538 0.084
## levelLocl:h 0.063 -0.069 -0.090 -0.583 0.066 0.635
## fldRVF:lvL: -0.045 0.084 0.066 0.430 -0.081 -0.799 -0.741
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00445801 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?
Using the bobyqa optimizer alone gives virtually the same
results.
summary(acc_model_ehi_bobyqa)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ field * level * ehi + (1 | subject)
## Data: aah_for_acc_ehi_model
## Control: glmerControl(optimizer = c("bobyqa"))
##
## AIC BIC logLik deviance df.resid
## 39113.4 39199.7 -19547.7 39095.4 108023
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -11.747602 0.117369 0.168279 0.238853 1.067891
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 1.05839 1.02878
## Number of obs: 108032, groups: subject, 844
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.9929178907 0.0532179046 75.02960 < 2e-16 ***
## fieldRVF -0.4208114420 0.0473856786 -8.88056 < 2e-16 ***
## levelLocal -0.9402494214 0.0439959119 -21.37129 < 2e-16 ***
## ehi -0.0006745785 0.0006575130 -1.02595 0.304913
## fieldRVF:levelLocal 0.5310456792 0.0593024543 8.95487 < 2e-16 ***
## fieldRVF:ehi 0.0000955453 0.0005978400 0.15982 0.873025
## levelLocal:ehi 0.0009996768 0.0005551421 1.80076 0.071741 .
## fieldRVF:levelLocal:ehi 0.0001862092 0.0007484593 0.24879 0.803523
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fldRVF lvlLcl ehi flRVF:L flRVF: lvlLc:
## fieldRVF -0.528
## levelLocal -0.575 0.635
## ehi -0.084 0.058 0.064
## fldRVF:lvlL 0.423 -0.799 -0.741 -0.046
## fieldRVF:eh 0.057 -0.105 -0.068 -0.538 0.084
## levelLocl:h 0.063 -0.068 -0.089 -0.583 0.066 0.635
## fldRVF:lvL: -0.045 0.084 0.066 0.430 -0.081 -0.799 -0.741
## optimizer (bobyqa) convergence code: 0 (OK)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?
Using a model with scaled EHI gives virtually the same results,
and no warning about large eigenvalues.
summary(acc_model_ehi_scaled)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ field * level * ehi + (1 | subject)
## Data: df_scaled
## Control: glmerControl(optimizer = c("bobyqa"))
##
## AIC BIC logLik deviance df.resid
## 39113.4 39199.7 -19547.7 39095.4 108023
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -11.748116 0.117364 0.168282 0.238852 1.067899
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 1.05841 1.02879
## Number of obs: 108032, groups: subject, 844
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.98957057 0.05297442 75.31126 < 2e-16 ***
## fieldRVF -0.42043214 0.04708796 -8.92866 < 2e-16 ***
## levelLocal -0.93523445 0.04377379 -21.36517 < 2e-16 ***
## ehi -0.05351304 0.05210742 -1.02698 0.30443
## fieldRVF:levelLocal 0.53211973 0.05901373 9.01688 < 2e-16 ***
## fieldRVF:ehi 0.00758447 0.04735701 0.16016 0.87276
## levelLocal:ehi 0.07929785 0.04397042 1.80344 0.07132 .
## fieldRVF:levelLocal:ehi 0.01477039 0.05927051 0.24920 0.80320
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fldRVF lvlLcl ehi flRVF:L flRVF: lvlLc:
## fieldRVF -0.526
## levelLocal -0.572 0.633
## ehi -0.021 0.023 0.026
## fldRVF:lvlL 0.420 -0.797 -0.740 -0.018
## fieldRVF:eh 0.023 -0.041 -0.027 -0.537 0.032
## levelLocl:h 0.026 -0.028 -0.025 -0.583 0.018 0.634
## fldRVF:lvL: -0.018 0.033 0.018 0.429 -0.016 -0.798 -0.740